{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Gaussian Mixture Model\n",
    "\n",
    "This tutorial demonstrates how to marginalize out discrete latent variables in NumPyro through the motivating example of a mixture model. We'll focus on the mechanics of parallel enumeration, keeping the model simple by training a trivial 1-D Gaussian model on a tiny 5-point dataset. See also the [enumeration tutorial](http://pyro.ai/examples/enumeration.html) for a broader introduction to parallel enumeration.\n",
    "\n",
    "#### Table of contents\n",
    "\n",
    "- [Overview](#Overview)\n",
    "- [Training a MAP estimator](#Training-a-MAP-estimator)\n",
    "- [Serving the model: predicting membership](#Serving-the-model:-predicting-membership)\n",
    "  - [Predicting membership using discrete inference](#Predicting-membership-using-discrete-inference)\n",
    "  - [Predicting membership by enumerating in the guide](#Predicting-membership-by-enumerating-in-the-guide)\n",
    "- [MCMC](#MCMC)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": [
    "!pip install -q numpyro@git+https://github.com/pyro-ppl/numpyro"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from collections import defaultdict\n",
    "import os\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import scipy.stats\n",
    "\n",
    "from jax import pure_callback, random\n",
    "import jax.numpy as jnp\n",
    "import optax\n",
    "\n",
    "import numpyro\n",
    "from numpyro import handlers\n",
    "from numpyro.contrib.funsor import config_enumerate, infer_discrete\n",
    "import numpyro.distributions as dist\n",
    "from numpyro.distributions import constraints\n",
    "from numpyro.infer import SVI, TraceEnum_ELBO, init_to_value\n",
    "from numpyro.infer.autoguide import AutoDelta\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "smoke_test = \"CI\" in os.environ\n",
    "assert numpyro.__version__.startswith(\"0.19.0\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Overview\n",
    "\n",
    "NumPyro's [TraceEnum_ELBO](https://num.pyro.ai/en/latest/svi.html#numpyro.infer.elbo.TraceEnum_ELBO) can automatically marginalize out variables in both the guide and the model. When enumerating guide variables, NumPyro enumerates in parallel by allocating on the left a new array dimension and using nonstandard evaluation to create an array of possible values at the variable's sample site. These nonstandard values are then replayed in the model. When enumerating variables in the model, the variables are enumerated in parallel and must not appear in the guide. Mathematically, guide-side enumeration simply reduces variance in stochastic ELBO estimates by exactly integrating out  an enumerated variable, whereas model-side enumeration avoids an application of Jensen's inequality by exactly marginalizing out an enumerated variable.\n",
    " \n",
    "Here is our tiny dataset. It has five points."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "No GPU/TPU found, falling back to CPU. (Set TF_CPP_MIN_LOG_LEVEL=0 and rerun for more info.)\n"
     ]
    }
   ],
   "source": [
    "data = jnp.array([0.0, 1.0, 10.0, 11.0, 12.0])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Training a MAP estimator\n",
    "\n",
    "Let's start by learning model parameters `weights`, `locs`, and `scale` given priors and data. We will learn point estimates of these using an [AutoDelta](https://num.pyro.ai/en/latest/autoguide.html#numpyro.infer.autoguide.AutoDelta) guide (named after its delta distributions). Our model will learn global mixture weights, the location of each mixture component, and a shared scale that is common to both components. During inference, [TraceEnum_ELBO](https://num.pyro.ai/en/latest/svi.html#numpyro.infer.elbo.TraceEnum_ELBO) will marginalize out the assignments of datapoints to clusters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "K = 2  # Fixed number of components.\n",
    "\n",
    "\n",
    "@config_enumerate\n",
    "def model(data):\n",
    "    # Global variables.\n",
    "    weights = numpyro.sample(\"weights\", dist.Dirichlet(0.5 * jnp.ones(K)))\n",
    "    scale = numpyro.sample(\"scale\", dist.LogNormal(0.0, 2.0))\n",
    "    with numpyro.plate(\"components\", K):\n",
    "        locs = numpyro.sample(\"locs\", dist.Normal(0.0, 10.0))\n",
    "\n",
    "    with numpyro.plate(\"data\", len(data)):\n",
    "        # Local variables.\n",
    "        assignment = numpyro.sample(\"assignment\", dist.Categorical(weights))\n",
    "        numpyro.sample(\"obs\", dist.Normal(locs[assignment], scale), obs=data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To run inference with this `(model,guide)` pair, we use NumPyro's [config_enumerate](https://num.pyro.ai/en/stable/funsor.html#numpyro.contrib.funsor.infer_util.config_enumerate) handler to enumerate over all assignments in each iteration. Since we've wrapped the batched Categorical assignments in a [numpyro.plate](https://num.pyro.ai/en/stable/primitives.html#numpyro.primitives.plate) independence context along the `data` batch dimension, this enumeration can happen in parallel: we enumerate only 2 possibilites, rather than `2**len(data) = 32`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Before inference we'll initialize to plausible values. Mixture models are very susceptible to local modes. A common approach is to choose the best among many random initializations, where the cluster means are initialized from random subsamples of the data. Since we're using an [AutoDelta](https://num.pyro.ai/en/latest/autoguide.html#numpyro.infer.autoguide.AutoDelta) guide, we can initialize by using a [init_to_value](https://num.pyro.ai/en/stable/utilities.html#numpyro.infer.initialization.init_to_value) helper function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "seed = 8, initial_loss = 25.149845123291016\n"
     ]
    }
   ],
   "source": [
    "elbo = TraceEnum_ELBO()\n",
    "\n",
    "\n",
    "def initialize(seed):\n",
    "    global global_guide\n",
    "    init_values = {\n",
    "        \"weights\": jnp.ones(K) / K,\n",
    "        \"scale\": jnp.sqrt(data.var() / 2),\n",
    "        \"locs\": data[\n",
    "            random.categorical(\n",
    "                random.PRNGKey(seed), jnp.ones(len(data)) / len(data), shape=(K,)\n",
    "            )\n",
    "        ],\n",
    "    }\n",
    "    global_model = handlers.block(\n",
    "        handlers.seed(model, random.PRNGKey(0)),\n",
    "        hide_fn=lambda site: site[\"name\"]\n",
    "        not in [\"weights\", \"scale\", \"locs\", \"components\"],\n",
    "    )\n",
    "    global_guide = AutoDelta(\n",
    "        global_model, init_loc_fn=init_to_value(values=init_values)\n",
    "    )\n",
    "    handlers.seed(global_guide, random.PRNGKey(0))(data)  # warm up the guide\n",
    "    return elbo.loss(random.PRNGKey(0), {}, model, global_guide, data)\n",
    "\n",
    "\n",
    "# Choose the best among 100 random initializations.\n",
    "loss, seed = min((initialize(seed), seed) for seed in range(100))\n",
    "initialize(seed)  # initialize the global_guide\n",
    "print(f\"seed = {seed}, initial_loss = {loss}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "During training, we’ll collect both losses and gradient norms to monitor convergence. We can do this using `hook_optax` helper function below."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Helper function to collect gradient norms during training\n",
    "def hook_optax(optimizer):\n",
    "    gradient_norms = defaultdict(list)\n",
    "\n",
    "    def append_grad(grad):\n",
    "        for name, g in grad.items():\n",
    "            gradient_norms[name].append(float(jnp.linalg.norm(g)))\n",
    "        return grad\n",
    "\n",
    "    def update_fn(grads, state, params=None):\n",
    "        grads = pure_callback(append_grad, grads, grads)\n",
    "        return optimizer.update(grads, state, params=params)\n",
    "\n",
    "    return optax.GradientTransformation(optimizer.init, update_fn), gradient_norms\n",
    "\n",
    "\n",
    "optim, gradient_norms = hook_optax(optax.adam(learning_rate=0.1, b1=0.8, b2=0.99))\n",
    "global_svi = SVI(model, global_guide, optim, loss=elbo)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now train the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|███████████████████████████████████████████████████████████████████████████| 200/200 [00:00<00:00, 287.42it/s, init loss: 25.1498, avg. loss [191-200]: 17.4433]\n"
     ]
    }
   ],
   "source": [
    "global_svi_result = global_svi.run(\n",
    "    random.PRNGKey(0), 200 if not smoke_test else 2, data\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 3), dpi=100).set_facecolor(\"white\")\n",
    "plt.plot(global_svi_result.losses)\n",
    "plt.xlabel(\"iters\")\n",
    "plt.ylabel(\"loss\")\n",
    "plt.yscale(\"log\")\n",
    "plt.title(\"Convergence of SVI\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4), dpi=100).set_facecolor(\"white\")\n",
    "for name, grad_norms in gradient_norms.items():\n",
    "    plt.plot(grad_norms, label=name)\n",
    "plt.xlabel(\"iters\")\n",
    "plt.ylabel(\"gradient norm\")\n",
    "plt.yscale(\"log\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.title(\"Gradient norms during SVI\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the learned parameters:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "weights = [0.375 0.625]\n",
      "locs = [ 0.4989534 10.984944 ]\n",
      "scale = 0.6514341831207275\n"
     ]
    }
   ],
   "source": [
    "map_estimates = global_svi_result.params\n",
    "weights = map_estimates[\"weights_auto_loc\"]\n",
    "locs = map_estimates[\"locs_auto_loc\"]\n",
    "scale = map_estimates[\"scale_auto_loc\"]\n",
    "print(f\"weights = {weights}\")\n",
    "print(f\"locs = {locs}\")\n",
    "print(f\"scale = {scale}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The model's `weights` are as expected, with about 2/5 of the data in the first component and 3/5 in the second component. Next let's visualize the mixture model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = jnp.arange(-3, 15, 0.1)\n",
    "Y1 = weights[0] * scipy.stats.norm.pdf((X - locs[0]) / scale)\n",
    "Y2 = weights[1] * scipy.stats.norm.pdf((X - locs[1]) / scale)\n",
    "\n",
    "plt.figure(figsize=(10, 4), dpi=100).set_facecolor(\"white\")\n",
    "plt.plot(X, Y1, \"r-\")\n",
    "plt.plot(X, Y2, \"b-\")\n",
    "plt.plot(X, Y1 + Y2, \"k--\")\n",
    "plt.plot(data, jnp.zeros(len(data)), \"k*\")\n",
    "plt.title(\"Density of two-component mixture model\")\n",
    "plt.ylabel(\"probability density\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally note that optimization with mixture models is non-convex and can often get stuck in local optima. For example in this tutorial, we observed that the mixture model gets stuck in an everthing-in-one-cluster hypothesis if `scale` is initialized to be too large.\n",
    "\n",
    "## Serving the model: predicting membership\n",
    "\n",
    "Now that we've trained a mixture model, we might want to use the model as a classifier. \n",
    "During training we marginalized out the assignment variables in the model. While this provides fast convergence, it prevents us from reading the cluster assignments from the guide. We'll discuss two options for treating the model as a classifier: first using [infer_discrete](https://num.pyro.ai/en/stable/funsor.html#numpyro.contrib.funsor.discrete.infer_discrete) (much faster) and second by training a secondary guide using enumeration inside SVI (slower but more general).\n",
    "\n",
    "### Predicting membership using discrete inference\n",
    "\n",
    "The fastest way to predict membership is to use the [infer_discrete](https://num.pyro.ai/en/stable/funsor.html#numpyro.contrib.funsor.discrete.infer_discrete) handler, together with `trace` and `replay`. Let's start out with a MAP classifier, setting `infer_discrete`'s temperature parameter to zero. For a deeper look at effect handlers like `trace`, `replay`, and `infer_discrete`, see the [effect handler tutorial](http://pyro.ai/examples/effect_handlers.html)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "trained_global_guide = handlers.substitute(\n",
    "    global_guide, global_svi_result.params\n",
    ")  # substitute trained params\n",
    "guide_trace = handlers.trace(trained_global_guide).get_trace(data)  # record the globals\n",
    "trained_model = handlers.replay(model, trace=guide_trace)  # replay the globals\n",
    "\n",
    "\n",
    "def classifier(data, temperature=0, rng_key=None):\n",
    "    inferred_model = infer_discrete(\n",
    "        trained_model, temperature=temperature, first_available_dim=-2, rng_key=rng_key\n",
    "    )  # set first_available_dim to avoid conflict with data plate\n",
    "    seeded_inferred_model = handlers.seed(inferred_model, random.PRNGKey(0))\n",
    "    trace = handlers.trace(seeded_inferred_model).get_trace(data)\n",
    "    return trace[\"assignment\"][\"value\"]\n",
    "\n",
    "\n",
    "print(classifier(data))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Indeed we can run this classifer on new data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_data = jnp.arange(-3, 15, 0.1)\n",
    "assignment = classifier(new_data)\n",
    "plt.figure(figsize=(8, 2), dpi=100).set_facecolor(\"white\")\n",
    "plt.plot(new_data, assignment)\n",
    "plt.title(\"MAP assignment\")\n",
    "plt.xlabel(\"data value\")\n",
    "plt.ylabel(\"class assignment\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To generate random posterior assignments rather than MAP assignments, we could set `temperature=1`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 1 1 1]\n"
     ]
    }
   ],
   "source": [
    "print(classifier(data, temperature=1, rng_key=random.PRNGKey(0)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the classes are very well separated, we zoom in to the boundary between classes, around 5.75."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x200 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "new_data = jnp.arange(5.5, 6.0, 0.005)\n",
    "assignment = classifier(new_data, temperature=1, rng_key=random.PRNGKey(0))\n",
    "plt.figure(figsize=(8, 2), dpi=100).set_facecolor(\"white\")\n",
    "plt.plot(new_data, assignment, \"x\", color=\"C0\")\n",
    "plt.title(\"Random posterior assignment\")\n",
    "plt.xlabel(\"data value\")\n",
    "plt.ylabel(\"class assignment\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Predicting membership by enumerating in the guide\n",
    "\n",
    "A second way to predict class membership is to enumerate in the guide. This doesn't work well for serving classifier models, since we need to run stochastic optimization for each new input data batch, but it is more general in that it can be embedded in larger variational models.\n",
    "\n",
    "To read cluster assignments from the guide, we'll define a new `full_guide` that fits both global parameters (as above) and local parameters (which were previously marginalized out). Since we've already learned good values for the global variables, we will block SVI from updating those by using [handlers.block](https://num.pyro.ai/en/stable/handlers.html#numpyro.handlers.block)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "@config_enumerate\n",
    "def full_guide(data):\n",
    "    # Global variables.\n",
    "    with handlers.block(\n",
    "        hide=[\"weights_auto_loc\", \"locs_auto_loc\", \"scale_auto_loc\"]\n",
    "    ):  # Keep our learned values of global parameters.\n",
    "        trained_global_guide(data)\n",
    "\n",
    "    # Local variables.\n",
    "    with numpyro.plate(\"data\", len(data)):\n",
    "        assignment_probs = numpyro.param(\n",
    "            \"assignment_probs\",\n",
    "            jnp.ones((len(data), K)) / K,\n",
    "            constraint=constraints.simplex,\n",
    "        )\n",
    "        numpyro.sample(\"assignment\", dist.Categorical(assignment_probs))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████████████████████████████████████████████████████████████████████| 200/200 [00:00<00:00, 298.62it/s, init loss: 338.6479, avg. loss [191-200]: 18.2659]\n"
     ]
    }
   ],
   "source": [
    "optim, gradient_norms = hook_optax(optax.adam(learning_rate=0.2, b1=0.8, b2=0.99))\n",
    "elbo = TraceEnum_ELBO()\n",
    "full_svi = SVI(model, full_guide, optim, loss=elbo)\n",
    "\n",
    "\n",
    "full_svi_result = full_svi.run(random.PRNGKey(0), 200 if not smoke_test else 2, data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 3), dpi=100).set_facecolor(\"white\")\n",
    "plt.plot(full_svi_result.losses)\n",
    "plt.xlabel(\"iters\")\n",
    "plt.ylabel(\"loss\")\n",
    "plt.yscale(\"log\")\n",
    "plt.title(\"Convergence of SVI\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(10, 4), dpi=100).set_facecolor(\"white\")\n",
    "for name, grad_norms in gradient_norms.items():\n",
    "    plt.plot(grad_norms, label=name)\n",
    "plt.xlabel(\"iters\")\n",
    "plt.ylabel(\"gradient norm\")\n",
    "plt.yscale(\"log\")\n",
    "plt.legend(loc=\"best\")\n",
    "plt.title(\"Gradient norms during SVI\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can now examine the guide's local `assignment_probs` variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "assignment_probs = full_svi_result.params[\"assignment_probs\"]\n",
    "plt.figure(figsize=(8, 3), dpi=100).set_facecolor(\"white\")\n",
    "plt.plot(\n",
    "    data,\n",
    "    assignment_probs[:, 0],\n",
    "    \"ro\",\n",
    "    label=f\"component with mean {locs[0]:0.2g}\",\n",
    ")\n",
    "plt.plot(\n",
    "    data,\n",
    "    assignment_probs[:, 1],\n",
    "    \"bo\",\n",
    "    label=f\"component with mean {locs[1]:0.2g}\",\n",
    ")\n",
    "plt.title(\"Mixture assignment probabilities\")\n",
    "plt.xlabel(\"data value\")\n",
    "plt.ylabel(\"assignment probability\")\n",
    "plt.legend(loc=\"center\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## MCMC\n",
    "\n",
    "Next we'll explore the full posterior over component parameters using collapsed NUTS, i.e. we'll use NUTS and marginalize out all discrete latent variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "sample: 100%|███████████████████████████████████████████████████████████████████████████| 300/300 [00:02<00:00, 130.21it/s, 7 steps of size 2.44e-01. acc. prob=0.41]\n"
     ]
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "                mean       std    median      5.0%     95.0%     n_eff     r_hat\n",
      "   locs[0]      2.45      4.30      0.62     -0.97     11.41      8.92      1.14\n",
      "   locs[1]      8.72      4.19     10.75      0.23     11.78      8.12      1.16\n",
      "     scale      1.58      1.75      1.02      0.57      3.46     19.19      1.02\n",
      "weights[0]      0.47      0.20      0.48      0.17      0.76      8.78      1.03\n",
      "weights[1]      0.53      0.20      0.52      0.24      0.83      8.78      1.03\n",
      "\n",
      "Number of divergences: 11\n"
     ]
    }
   ],
   "source": [
    "from numpyro.infer import MCMC, NUTS\n",
    "\n",
    "kernel = NUTS(model)\n",
    "mcmc = MCMC(kernel, num_warmup=50, num_samples=250)\n",
    "mcmc.run(random.PRNGKey(2), data)\n",
    "mcmc.print_summary()\n",
    "posterior_samples = mcmc.get_samples()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "X, Y = posterior_samples[\"locs\"].T"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 8), dpi=100).set_facecolor(\"white\")\n",
    "h, xs, ys, image = plt.hist2d(X, Y, bins=[20, 20])\n",
    "plt.contour(\n",
    "    jnp.log(h + 3).T,\n",
    "    extent=[xs.min(), xs.max(), ys.min(), ys.max()],\n",
    "    colors=\"white\",\n",
    "    alpha=0.8,\n",
    ")\n",
    "plt.title(\"Posterior density as estimated by collapsed NUTS\")\n",
    "plt.xlabel(\"loc of component 0\")\n",
    "plt.ylabel(\"loc of component 1\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that due to nonidentifiability of the mixture components the likelihood landscape has two equally likely modes, near `(11,0.5)` and `(0.5,11)`. NUTS has difficulty switching between the two modes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x300 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 3), dpi=100).set_facecolor(\"white\")\n",
    "plt.plot(X, color=\"red\")\n",
    "plt.plot(Y, color=\"blue\")\n",
    "plt.xlabel(\"NUTS step\")\n",
    "plt.ylabel(\"loc\")\n",
    "plt.title(\"Trace plot of loc parameter during NUTS inference\")\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.16"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
